Degenerate branching

In the oxidation of PX and MX, formaldehyde is a degenerate branching intermediate, whereas phthalan is formed from OX ... 

The reaction with sulfides occurs efficiently only when the resulting carbon-centered radicals are further stabilized by a a-heteroatom. Indeed, (TMSfsSiH can induce the efficient radical chain monoreduction of 1,3-dithiolane, 1,3-dithiane, 1,3-oxathiolane, 1,3-oxathiolanone, and 1,3-thiazolidine derivatives. Three examples are outlined in Reaction (12). The reaction of benzothiazole sulfenamide with (TMS)3SiH, initiated by the decomposition of AIBN at 76 °C, is an efficient chain process producing the corresponding dialkylamine quantitatively. However, the mechanism of this chain reaction is complex as it is also an example of a degenerate-branched chain process. 

Semenov put forward the concept of slow hydrocarbon oxidation as the chain reaction with degenerate branching N. N. Semenov [49]... 

As already noted (see Chapter 4), autoxidation is a degenerate branching chain reaction with a positive feedback via hydroperoxide the oxidation of RH produces ROOH that acts as an initiator of oxidation. The characteristic features of inhibited autoxidation, which are primarily due to this feedback, are the following [18,21,23,26,31-33] ... 

Since the system requires the buildup of ROOH and R CHO before chain branching occurs to a sufficient degree to dominate the system, Semenov termed these steps degenerate branching. This buildup time, indeed, appears to account for the experimental induction times noted in hydrocarbon combustion systems. It is important to emphasize that this mechanism is a low-temperature scheme and consequently does not include the high-temperature H2—02 chain branching steps. 

The re-oxidation of lead was expected to occur rapidly at 600 K the surface of the lead oxide would then remain unchanged in the presence of oxygen. The authors concluded that, as a consequence, general hydrocarbon combustion in which formaldehyde is a degenerate branching intermediate is inhibited in the presence of PbO by the rapid removal of formaldehyde. 

Figure 6 shows the variation of peroxide concentration in methyl ethyl ketone slow combustion, and similar results, but with no peracid formed, have been found for acetone and diethyl ketone. The concentrations of the organic peroxy compounds run parallel to the rate of reaction, but the hydrogen peroxide concentration increases to a steady value. There thus seems little doubt that the degenerate branching intermediates at low temperatures are the alkyl hydroperoxides, and with methyl ethyl ketone, peracetic acid also. The tvfo types of cool flames given by methyl ethyl ketone may arise from the twin branching intermediates (1) observed in its combustion. 

In recent years Emanuel, Neiman, and their respective schools have greatly contributed to the theory of antioxidant action by studying the phenomenon of the critical antioxidant concentration in terms of a degenerate branched chain reaction. The critical antioxidant concentration, a well-established feature of phenolic antioxidants, is one below which autoxidation is autocatalytic and above which it proceeds at a slow and steady rate. Since the theory allowed not only a satisfactory explanation of the critical antioxidant concentration itself but elucidation of many refinements, such as the greater than expected activity of multifunctional phenolic antioxidants (21), we wondered whether catalyst-inhibitor conversion could be fitted into its framework. If degenerate chain branching is assumed to be the result of... 

It is clear that the concept of formaldehyde as the relatively stable intermediate responsible for degenerate branching is a fundamental one in elaborating the kinetics of methane oxidation. Indeed the statement has been made (64) that the combustion of methane may be regarded as the formation and oxidation of formaldehyde. 

The reaction starts at a low rate as shown by the rate of pressure change and accelerates in the manner commonly associated with degenerate branching. 

If it is accepted that the activation energy of a chain reaction is largely that of the process generating chains, then the parallelism in the behavior of the energies of activation for the ethylene and formaldehyde oxidations may be interpreted on the basis of the degenerate-branching reaction the former is identical with the initiation reaction for the latter. Two possible reactions were suggested... 

The mode of formation of formaldehyde is of interest in the case of cyclopropane oxidation. The mechanism advanced involved a complex rearrangement of the cyclo-propylperoxy radical to formaldehyde and CH3CO. The degenerate-branching reaction of formaldehyde was formulated on the following considerations. Lead oxide which markedly inhibits the oxidation of methane (26), presumably by efficient heterogeneous destruction of H02 radicals, is known to exert a similar effect on cyclopropane combustion... 

For branching to occur a > 1, and can often be 2 or 3, though rarely greater. There are occasions (see Section 6.15 on degenerate branching) where a is just slightly greater than unity, and under these circumstances a different situation will occur. 

Cool flame behaviour is the result of highly limited degenerate branching, where the branching coefficient, a, is small, e.g. is of the order of 1.1, compared with being of the order of two or three in normal branching. 

For mixtures between b and c luminescence would appear in the vessel, the temperature and pressure would show a sudden jump and there would be an audible click. This is the cool flame region, where degenerate branching becomes dominant. If not all the reactant is used up in the first cool flame... 

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